Engineering Structures 26 (2004) 2137–2148 www.elsevier.com/locate/engstruct Structural models of critical regions in old-type r.c. frames with smooth rebars Giovanni Fabbrocino
, Gerardo M. Verderame, Gaetano Manfredi, Edoardo Cosenza Department of Structural Analysis and Design, University of Naples Federico II, Via Claudio, 21, 80125 Napoli, Italy Received 19 February 2004; received in revised form 29 July 2004; accepted 29 July 2004 Abstract Structural assessment of existing reinforced concrete constructions under gravity loads and seismic actions has a high social and economical impact; actually in many European countries, most of the buildings dates back to 1960s and 1970s and cannot ensure satisfactory seismic response, since many areas have been later classified as seismic or since design has been carried out according to obsolete codes. These structures are generally reinforced with smooth bars that exhibit poor bond and need specific anchoring end details. In the present paper, some key aspects of structural models of smooth reinforcement for old-type r.c. frame analysis are reported. Results of experimental tests on smooth reinforcement and circular hook anchoring devices are also used to discuss some aspects of behavioural models of beam to column critical regions. # 2004 Elsevier Ltd. All rights reserved. Keywords: Old-type r.c. structures; Seismic assessment; Smooth rebars; Bond; Anchorage details 1. Introduction A large number of existing reinforced concrete buildings in Europe is located in seismic areas, and has been designed according to obsolete seismic codes or taking into consideration only gravity loads (GLD structures). This circumstance makes very relevant the issue of structural assessment in view of seismic strengthening of existing structures. Actually, a strong effort has been carried out in many countries to improve the reliability of seismic design of new structures, resulting in an increased knowledge of non-linear behaviour of concrete structures and cyclic response of members under seismic actions. This knowledge represents an essential background for structural evaluation of existing structures, but refers generally to concrete constructions reinforced with deformed bars, so that influence of smooth bars on the non-linear response of members and critical regions is not fully established. Some experimental researches have been devoted to assess global perfor
Corresponding author. Tel./fax: +39-081-7683424. E-mail address: giovanni.fabbrocino@unina.it (G. Fabbrocino). 0141-0296/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2004.07.018 mances of old-type structures [1], but local aspects, i.e. bond, were not exhaustively investigated. The latter are predominant critical regions, i.e. beam to column joints, are considered, since complex mechanical interactions develop with very high gradients due to mechanical actions applied at the connected end sections, as sketched in Fig. 1, where stresses and deformations on concrete panel and steel rebars are separately reported. Concrete panel mechanism is related to cracking of concrete and arrangement of transverse reinforcement in the joint region; while slippage of anchored Fig. 1. Mechanisms governing the joint region deformation: panel (a), bar slip (b). 2138 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 reinforcement is dependent on bond properties and anchoring details and leads to a rotation of member end section that is commonly addressed as fixed-end rotation. The above-mentioned sources of deformation could be generally neglected if structural analysis is aimed to evaluate the ultimate strength capacity of r.c. frames with deformed bars, but have a key role when drift capacity is concerned, as confirmed by theoretical– experimental comparisons [2]. This circumstance is clearly shown in Fig. 2, where numerical analyses carried out on a r.c. frame have been devoted to point out the effect of bond and fixed-end rotation on base shear coefficient-top drift response. It is easy to recognise that fixed-end rotation becomes predominant in the frame response mainly when smooth rebars are used. In this case, structural modelling becomes more complex since bond of reinforcement and behaviour of anchoring devices at rebar ends are essential to assess structural performances of old-type constructions. A critical review of available technical literature has shown that the knowledge on plain bars behaviour and in particular on bond and on mechanical response of anchoring details is poor. In fact, many 50 years old and even older experimental results on plain bars can be found, but they are basically presented as reference data for deformed bars; furthermore, their relevance for present analyses is limited due to lack of technical Fig. 2. Comparative results on effect of type of reinforcement on drift capacity. Fig. 3. capabilities, since tests were carried out in force control mode, missing large post-yielding phases and information about descending branches. However, an attempt to model the response of anchored rebars can be carried out referring to Fig. 3 that reports in detail the idealised force transfer mechanism governing the behaviour of the anchored reinforcing bar under tension. The latter can be divided into two components, the straight region and the anchorage, represented by a circular hook. From a theoretical point of view, the end anchorage results in a restraint for the inner end of straight rebar, where two boundary conditions can be identified: free inner end of the rebar, so that a slippage develops; rigid inner end with zero rebar slip, leading to a pull-out force, Fhook, on the anchoring device. In the first case, pull-out strength is due to bond properties of smooth bars resulting in very low bar strain compared to yielding level; in the second case, high ratios between applied force and anchorage reaction can be reached, even 50–60% of the applied tensile force. Behaviour of anchoring device obviously influences the strength and deformation response of the member end sections. In fact, pull-out of smooth bars without anchoring devices leads to the premature failure of the member end section; conversely, rigid anchorage allows the full development of flexural strength and produces the minimum value of slippage at the loaded end [3]. As a result, the actual stress–slip response of an anchored bar lays in the shaded area of Fig. 3; so the key issue in a reliable modelling of r.c. frames for seismic assessment is the definition of the relationship between the axial force applied on the anchorage and the slippage of its loaded end in view of the development of a behavioural model of the anchored bar. The present paper is aimed to discuss the main aspects of the structural response of old-type r.c. members and critical regions detailed according to 1960s practice, taking into account the influence of bond properties of hooked and straight bars. Behaviour of anchored smooth bars is examined referring to basic Stress vs. loaded end slip of anchored smooth bars. G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 properties of bond and response of bar end details used in critical regions. The attention is focussed on circular hooks and on their stress–slip response under static loads. This behaviour influences the seismic capacity of exterior and interior beam to column connections; in the first case, the main influence on the fixed-end rotation response is given by the anchored rebar, which is characterised by a global response, i.e. in terms of stress vs. slip relation, dependent upon end detail deformation. The results of experimental tests on reinforcement local stress–slip response are used to analyse fixed-end rotation of r.c. beams where smooth rebars are provided. When interior beam to column connections are concerned, the presence of continuous rebars plays a relevant role, so that refined modelling of the joint and of the element end section are needed. In fact, smooth reinforcement can lead to steel strains in the concrete compression zone quite different from classical Bernoulli’s hypothesis. On this specific aspect, an overview of the main numerical results will be given, pointing out some key aspects of strength and ductility development in existing underdesigned r.c. frames under seismic loading condition. 2. Experimental results on straight and hooked smooth bars 2.1. Bond of smooth bars Bond of smooth bars has been investigated firstly by modified beam tests [2] and then by pull-out tests, properly modified in order to avoid compressive stresses on the concrete component. In fact, as shown in Fig. 4b, the concrete specimens used for pull-out tests are restrained by studs on lateral surfaces so that the upper surface can fit the stress conditions of cracked concrete sections. Measurements of loaded and unloaded end have been taken; in this way, it has been 2139 recognised that the scatter between the two measures is negligible if compared with similar tests on deformed rebars. In Fig. 4a, some experimental results in terms of mean bond stress vs. mean slip are shown. The embedded length is 10 times the bar diameter. Results of pull-out tests are similar to beam test one, a peak bond stress of about 1.75 MPa at a mean slip of 0.18 mm has been reached. The comparison between the MC 90 [4] bond–slip relationships shows that the experimental peak bond stress can be predicted using good bond provisions, while residual stresses are well fitted referring to poor bond conditions. Cycles performed at a large slip level show the response of smooth bars to reversal actions, activating a significant degradation of bond. 2.2. Stress–slip relationship for circular hooks As already mentioned, modelling of anchored bars requires the knowledge of mechanical response of each component: the straight smooth bar and the anchoring detail. The latter generally depends on national codes and/or practice, thus a comprehensive critical review of former International codes, design manuals [5] and design drawings referring to existing buildings has been carried out in order to identify typical solutions. It has v been found that hooks with 180 opening angle can be addressed as the most common anchoring solution when smooth bars are concerned. Its geometry is defined starting from the ratios Dh/U and Lst/U, where Dh is the circular branch internal diameter, Lst is the length of the straight end branch and U is the bar diameter. Typical values of Dh/U and Lst/U ratios in existing constructions are 5 and 3, respectively, and have been used to define the geometry of bar anchorages analysed from an experimental point of view, as shown in Fig. 5b. Pull-out type tests have been carried out to evaluate the response in terms of force/stress–slip relationship of hooks; the tests have been designed in such a way Fig. 4. Experimental results of pull-out tests on smooth bars. G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 2140 rebars and are given in terms of rhook–shook relationship; three types of specimens are reported depending on the cast direction: a-type, representative of top beam reinforcement, b-type representative of column footing zone, c-type representative of lower beam reinforcement. The main results of the tests can be summarised referring to Fig. 5a as follows: – hook exhibits a very high initial stiffness and then a strongly non-linear behaviour even at low stress levels; – the stress–slip response is not characterised at yielding by the well-known plastic plateau of mild steel rebars; this circumstance is due to the limited yielding spreading along the circular branch, so that yielding develops only in the straight unbonded region. – the slip increases as the stress increases due to strain hardening, resulting in a progressive degradation of anchorage stiffness up to steel failure. 3. Theoretical stress–slip formulation of 180 circular hooks Fig. 5. v Stress vs. slip relationship of 180 smooth hooks. that a direct measure of the slip at the end section of the circular branch could be taken using a high performance wire potentiometer. The main investigated parameters of the experimental analysis are the concrete cover thickness, the cast direction and the type of loading (static or cyclic). A detailed description of test setup and of experimental results is reported in Ref. [6]; in the following, the main aspects of the experimental study will be briefly summarised. To this end, Fig. 5 gives an overview of experimental results and reports a picture of the concrete specimen. The results refer to 12 mm v The definition of a theoretical stress–slip relationship has to be based on the main aspects of the experimental behaviour previously discussed. The evaluation of experimental curve shapes and plot of functions commonly used in literature to fit similar phenomena, i.e. bond [7], shear connectors in composite constructions [8], allow to recognise the basic requirements of a theoretical formulation of stress–slip relationship for circular hooks: experimental curves are basically continuous, so a single curve formulation is reliable; ultimate stress and slip at bar failure can be used as basic parameters of the theoretical formulation; the first one is an hexogen parameter, depending upon the steel grade, the second one can be evaluated using a statistical analysis of available test results. It is easy to recognise that the constitutive law by Popov [9], proposed for bond fulfils the above requirements; in fact, it is based on the following relation:
 shook a rhook ðsÞ ¼ fu  ð1Þ su where rhook is the hook slip, shook is the hook stress at bar failure, fu is the bar ultimate stress and a is a dimensionless positive exponent that is generally lower than 1. Characterisation of theoretical formulation requires the definition of two parameters, the ultimate hook slip su and the exponent a, able to minimize the error function: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  exp 2 P  snum i i¼1;n si ð2Þ n1 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 where sexp is the experimental value of hooks slip at a i num given stress level, rexp is the numerical hook slip i ; si calculated according to (1) at the rexp stress level and i exp finally n is the number of experimental data (sexp i ;ri ). In Fig. 6, the comparison between the experimental curves and the optimal constitutive law is reported for all the type of pull-out specimens; in particular, in Fig. 6a, c and e, the shapes of the error function vs. the experimental slips are plotted depending on the value of exponent a. It is worth noting that the adopted constitutive law is really able to fit the experimental behaviour. In Fig. 7, all the experimental curves are Fig. 6. 2141 plotted and the optimal curve derived from the statistical analysis of all experimental data is reported. Finally, Fig. 8 reports the constitutive laws evaluated with reference to different type of specimens; it is worth noting that hooks that are perpendicular to the cast direction with the circular branch installed downward (beam upper reinforcement) show a stiffer behaviour respect to the remaining geometries, like vertical bars (column reinforcement), horizontal hooks installed upwards (lower beam reinforcement). The results of the parameter optimisation is reported in Table 1, where the values of a and of the slip, su, at the steel failure are given. Theoretical–experimental comparison depending on the type of test. 2142 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 Fig. 7. Theoretical–experimental comparison plotted for all tests. 4. External beam to column joints The results discussed in the previous section can be used to evaluate the behaviour of the beam to column connection, with specific reference to the fixed-end rotation, that is the main source of deformation in the case of external beam to column joint. In particular, the already discussed distinct mechanical characterisation of the two components, Fig. 9a, enables the development of a reliable numerical procedure to fit stress–slip relationship of anchored bars at the joint–element interface section. The calibration of numerical results has been carried out with reference to a series of pull-out tests on fullbonded specimens are presented and discussed. The test-setup is shown in Fig. 9b; the geometry of the hook and of the rebar are the same of Fig. 5b, while the length of the bonded straight region is 210 mm. Two tests have been carried out in displacement control and measures of bar strain, applied load and slippage of the rebar located on the top surface of the specimen have been taken. Fig. 9c shows the results of two tests on 12 mm bars in terms of stress–slip relationships. It is easy to recognise that the mechanical response is non-linear even for low stress levels with small slip values in the elastic region. When yielding stress is reached, a sudden increase of bar slip occurs exhibiting a plastic plateau on the analogy with the plain rebar. This remarks show that a degradation of bond occurs, since plastic plateau can be only related to a yielding spreading in the embedded region. In order to analyse this specific aspect, some numerical simulations of the anchored rebar are compared with experimental data. Numerical results are obtained as follows: 1. stress–slip relationship for hooked region is assumed as discussed in Section 3; shape values a and su are those evaluated for all specimens. 2. stress–slip for bond comes from fitting of experimental data. Two calculated curves are reported; the first one is derived assuming a bond relation obtained from pullout tests with a constant residual stress (continuous curve); the second one is characterised by a degradation of bond that starts as yielding takes place (dashed curve). The latter seems to fit better experimental data. Further developments are needed in order to clarify some aspects of the degradation mechanisms shown during the tests. Anyhow, these results allow to discuss the Table 1 Summary of optimised parameters of the theoretical stress–slip law Fig. 8. Theoretical formulation of stress–slip relationships. Reference test groups a su (a) (b) (c) All 0.30 0.25 0.37 0.30 4.10 3.10 4.00 3.90 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 2143 Fig. 9. Influence of anchored rebar deformation on the external beam to column connection. influence of bond properties and hooked end details of the rebars on the response in terms of moment– rotation at the end of the members. In fact, the knowledge of the constitutive relationship in terms of flexural behaviour of the member end section leads to the definition of a rational evaluation of the fixed-end rotation at the external beam to column joint. The definition of the moment–rotation relationship requires the calculation of the moment–curvature relation of the member end section and the performances of anchored rebars; in fact, the first calculation can give the position of the neutral axis and the stress acting on the rebars depending on the applied bending moment. As a result, moment–rotation curve of the end section depends on local properties of anchored rebars. Fig. 9d shows an example of such moment–rotation relationship. The curves are calculated assuming the theoretical solutions of the anchored reinforcement discussed above and a rectangular cross-section 300 by 500 mm with ð5 þ 5ÞU12 mm reinforcing bars, whose mechanical properties are the one of pull-out test rebars. The member end section exhibits a considerable deformability that cannot be neglected; it is also shown that the plastic plateau plays an important role especially between yielding and strain hardening initiation. This is a key issue of such modelling, since due to material and specific GLD frames properties, failure of members is generally due to concrete failure, with reinforcement that is beyond the yielding strain, but does not reach the strain hardening branch. 5. Interior beam to column joints Structural response in terms of flexural strength and deformation of the member end sections at interior beam to column joints depends basically on bond performances of reinforcement. In fact, rebars commonly pass through the panel region and anchoring devices are located at the end of the elements. This condition is schematically reported in Fig. 10a, where the load condition of reinforcement is also represented. When seismic actions are concerned, longitudinal reinforcement of members that cross the nodal region are subjected, if Bernoulli’s hypothesis is fulfilled, to a push–pull loading condition (Fig. 10b). As a consequence, the resultant of forces acting on the rebar have to be transferred by bond to surrounding concrete. This transfer action results can be reduced be in the case of smooth rebars and, as consequence, the strength and deformation capacity of end member section at internal joints decreases [10]. Assuming a constant distribution of bond stresses along the rebar, the ratio between the stresses acting at G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 2144 Fig. 10. (a) Bond mechanism in interior beam to column joint. (b) Plot of the ratio r0s =rs depending on the stress applied on rebars under tension. the rebar ends is given by: a¼ r0s rs ¼1 4  sb Ht rs  U ð3Þ where U is the bar diameter and the other symbols can be identified referring to Fig. 10a. Eq. (3) is plotted in Fig. 10b, that is defined assuming a given ratio between the beam height and the bar diameter, Ht/U and a uniform distribution of bond stresses, sb. These curves are compared with the relation r0s =rs obtained from a Bernoulli analysis, r0s ¼ f ðrs ;Xc Þ curve. The comparison between the abovementioned curves clearly shows that the Bernoulli hypothesis can be fulfilled only at low stress levels; increasing the tensile stress rs, the translational equilibrium of the bar under the bond stress is not satisfied. The influence of compressive stress on smooth reinforcement passing through a nodal region can be evaluated according to a cinematic model that removes some usual assumptions on the deformation of members cross-section. In fact, it is assumed that strains of concrete subjected to compressive stresses and of rebars under tension lay on a straight line; this is the way the curvature can be evaluated. Furthermore, it is assumed that a slip at the rebar–concrete interface occurs and that part of tensile stresses migrates to concrete in the so-called effective area of the cross-section [11]. Equations that solve the problem are as follows: . Equation of longitudinal equilibrium of the crosssection; ð rc ðx;yÞ  dA þ r0s ðx;yÞ  A0s  rct  Aeff Ac  rs ðx;yÞ  As ¼ NðzÞ section; ð rc ðx;yÞ  y  dA þ r0s ðx;yÞ  A0s  d0 s  rct  Aeff ð4Þ . Equation of global rotational equilibrium evaluated with reference to the centroid of the gross cross- Ac  dct  rs ðx;yÞ  As  ds ¼ MðzÞ ð5Þ Constitutive relationships have to be taken into account to relate static and cinematic parameters of materials (concrete under tension and compression, reinforcement): rs ¼ rs ðes Þ ð6aÞ rc ¼ rc ðec Þ ð6bÞ r0s ð6cÞ ¼ r0s ðe0s Þ rct ¼ rct ðect Þ ð6dÞ Eqs. (4) and (5) exhibit four unknown strain ec, ect, e0s and es. As a consequence, the relationship between moment and curvature is not a one to one function, but depends upon two variables, concrete in tension strain, ect and reinforcement namely under compression one, e0s ; both values are dependent on the interaction phenomena (bond) that takes place in the r.c. member. If post-cracking phase is concerned, stress acting in the cross-section cracked concrete region fulfils the following relationship ect ¼ 0. In this way one of the two unknown parameters is given, but strain acting on the reinforcing bar namely under compression, e0s , cannot be still evaluated. However, referring to Fig. 11, the above-mentioned bond mechanism acting on the rebars passing through the nodal region enables the definition of a one to one relationship with the stress acting on the other bar end section, rs. In fact, the following relationship can be written: drs ðzÞ 4 ¼  sb ðzÞ dz U ð7Þ and has to be associated to the bond–stress relationship: sb ¼ sb ðsÞ ð8Þ G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 2145 Fig. 11. Behavioural model of the cross-section at the element–concrete panel interface. If a rigid-perfectly plastic bond–slip relationship is assumed for smooth bars, a correlation between the stresses at the ends of the passing through reinforcement, r0s and rs (or e0s and es), can be evaluated. In the following, some results of numerical analyses carried out on a r.c. cross-section depending on the value of the stress r0s are presented. This stress varies between the value calculated according to a conventional analysis (Bernoulli’s hypothesis) and the ultimate tensile stress, fu, of the bar. In particular, attention is focussed on main static and cinematic parameters of the section, as moment and curvature both at ultimate and yielding conditions. Fig. 12a and b shows the M–N interaction curves at yielding and at ultimate state of failure in the region of compression. They are dependent upon the stress level, r0s , of the reinforcing bars namely under compression. Four values of r0s are considered: Bernoulli reference stress, zero, tensile yielding stress fy, ultimate tensile stress, fu. Plots (a) and (b) show also the reference M– N interaction curve evaluated according to Bernoulli’s hypothesis. If axial load N is given, both yielding and ultimate bending moments change depending on the stress r0s ; it is easy to recognise that the higher is the stress in the rebars namely under compression, the lower is the corresponding bending moment. Comparing data depending on r0s and the reference interaction curve (Bernoulli), it can be observed that the scatter is negligible for low axial loads, 10% of the ultimate Nu or lower, but significantly increases as the axial load increases. In summary, stress r0s acting on the reinforcing bars namely under compression plays a relevant role in the development of strength mechanisms of the cross-section, especially when high axial loads are concerned. A reduction of about 30% of the flexural resistance can take place. Similar plots are shown in Fig. 12c and d regarding the curvature of the section at yielding, /y, and failure, /u, respectively. The local ductility of the cross-section given by the ratio /u//y is reported in Fig. 12e. The progressive loss of compression of the rebars leads to a slight increase of the curvature at yielding compared with the one given by Bernoulli’s analysis; the higher is the axial load the higher is the scatter between the two above data. Conversely, tensile stresses in the rebar lead to a reduction of the curvature at failure respect to the one after Bernoulli. This scatter decreases as the axial load increases. A similar trend can be recognised for the curvature at failure. In order to estimate the influence of this phenomenon on the global response of a structural system, a sample structural assembly is analysed; it is actually interesting in all cases of regular structures, since its response can be easily related to global displacement capacity of the frame [12]; this is why it is also frequently used in many experimental studies. The assembly is reported in Fig. 13b; for the sake of simplicity, both geometry and applied forces are assumed as symmetrical. The square columns are 300 mm wide; ð3 þ 3ÞU12 rebars are provided. Beams are rectangular 300 500 mm; ð5 þ 5ÞU12 reinforcing bars are provided. Axial load applied on the column is assumed constant and equal to 540 kN. Three reinforcement arrangements are taken into account: (a) beam and column reinforcing rebars are anchored in the nodal region using circular hooks; (b) beam and column reinforcing rebars pass through the nodal region; (c) beam reinforcing rebars are anchored in the nodal region and column reinforcing rebars pass through the nodal region. A non-linear analysis of the assembly is carried out taking into account the concrete cracking and the distribution of yielding; push–over curves corresponding to different reinforcement arrangement are plotted in Fig. 13c. In order to point out the contribution of local member ductility on global response of the assembly fixedend rotation and panel deformation are neglected. The latter contribution strongly increases when concrete cracking occurs; this circumstance can be a priori excluded due to dimensions and mechanical properties 2146 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 Fig. 12. Influence of stress level r0s on main static and cinematic parameters of the section: (a) yielding moment, (b) ultimate moment, (c) yielding curvature, (d) ultimate curvature, (e) cross-section schematic view, and (f) curvature ductility. of material. Fragile shear failure of concurrent members can be excluded as well. Strength and ductility of member end cross-sections (beams and columns) are evaluated on the basis of two distinct assumptions. Firstly, it is assumed that con- crete and reinforcement strains are the same in compliance with Bernoulli’s analysis applied to r.c. structures (defined full interaction), then slippage of rebar respect to surrounding concrete is considered; the latter condition is defined in the following ‘partial G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 2147 Fig. 13. Representative r.c. frame assembly (a, b) and results of push–over analyses (c). interaction’. Table 2 summarises values of bending moments, ultimate curvature and ductility of the crosssection depending on the above assumptions. Three push–over analyses are carried out depending on reference model and the reinforcement arrangement, in particular: 1. conventional analysis for both end sections (arrangement a); 2. partial interaction for both end cross-sections (arrangement b); 3. partial interaction for column and conventional analysis for beam (arrangement c). Fig. 13c shows push–over results for column shear vs. drift. Analysis made according to the first assumption (arrangement a) shows the maximum column shear Vc ¼ 62:5 kN and maximum drift (1.32%) that are related to the local failure of the beam end section. Partial interaction between both interface sections (beam and column) leads to a maximum column shear that is not so different with respect to the one evaluated according to assumption #1, but columns drift (0.80%) is dramatically reduced. This result points out from a global standpoint the deterioration of mechanical properties of interface cross-sections due to partial interaction that are more relevant in terms of ultimate Table 2 Summary of results in terms of main static and cinematic parameters Parameter Beam Column My Mu /u l/ My Mu /u l/ (kN m) (kN m) (1/m) (kN m) (kN m) (1/m) Full interaction Partial interaction Scatter (%) 78.42 92.94 0.110 25.40 80.56 86.38 0.041 3.53 74.67 84.25 0.071 14.78 74.61 78.06 0.031 2.43 5 9 35 42 7 10 24 31 2148 G. Fabbrocino et al. / Engineering Structures 26 (2004) 2137–2148 curvature than in terms of ultimate bending moment. It is worth noting that local failure is attained in the joint–beam interface section due to the concrete failure strain assumed as already mentioned equal to ecu ¼ 0:0035 for the sake of simplicity. Analysis made according to the third assumption (arrangement c) shows a response that is intermediate between the preceding ones. In any case, it is actually interesting since anchored rebars in the joint regions is a reinforcement detailing commonly used in existing buildings made of concrete reinforced with smooth rebars. Anyhow, deterioration of mechanical properties at the column interface section only leads to the column failure rather than beam failure like in the other two hypotheses, changing the failure mode of the assembly. 6. Conclusions The paper discusses some key issues in the seismic assessment of old-type r.c. frames. In particular, the attention has been focussed on the influence of bond performances of smooth rebars on ductility and strength of critical regions, i.e. beam to column or base column regions. v Pull-out tests on straight rebars and 180 circular hooks have been briefly described and a generalized formulation, representing the response of the end details, has been used to calibrate a model of an anchored rebar generally used in external beam to column joint region. The results show the relevant role of anchoring devices, but also of the straight region characterised by poor bond performances especially in large post-yielding phase, as clearly shown by the experimental– numerical comparison. If internal joint regions are concerned, experimental background has been used to develop a behavioural model of the joint, in particular of the connected member end sections: thus, the effects of distribution of stresses along the rebars passing through the nodal region on the global response of a cruciform subassemblage have been estimated. Numerical results based on simplified, but reliable, assumptions show that strength is less sensitive respect to the ductility when the stress of reinforcement in compression changes its value due to push–pull action on the rebar. Comparisons between conventional and enhanced analyses show that partial interaction due to poor bond of smooth rebars can reduce the ductility up to 40%. This effect has been also recognised at global level. References [1] fib Task Group 7.1. State of the Art Report. Seismic assessment and retrofit of reinforced concrete buildings. fib Bulletin No. 24, May 2003. [2] Cosenza E, Manfredi G, Verderame GM. Seismic assessment of gravity load designed r.c. frames: critical issues in structural modeling. Journal of Earthquake Engineering 2002;6(1). [3] Fabbrocino G, Verderame GM, Manfredi G. Experimental behaviour of straight and hooked smooth bars in existing r.c. buildings. Proceedings of the 12th European Conference on Earthquake Engineering, London. 2002. [4] CEB-FIP Model Code 1990. Design Code-Comite Euro-International du Beton 1991. [5] Santarella L. Il cemento armato—La tecnica e la statica. Milano: Hoepli; 1937 [in Italian]. [6] Fabbrocino G, Verderame GM, Manfredi G, Cosenza E. Experimental response and behavioural modelling of anchored smooth bars in existing RC frames. Bond in concrete—from research to standards, Budapest, 2002. [7] Eligehausen R, Popov EP, Bertero VV. Local bond–stress relationships of deformed bars under generalised excitations. UCB/ EERC 83, 23, 1983. [8] Ollgard JG, Slutter RG, Fisher JW. Shear strength of stud connectors in lightweight and normal weight concrete. AISC Engineering Journal 1971;8(2):55–64. [9] Popov EP. Bond and anchorage of reinforcing bars under cyclic loading. ACI Structural Journal 1984;81(4):340–9. [10] Hakuto S, Park R, Tanaka H. Effect of deterioration of bond of beam bars passing through interior beam–column joints on flexural strength and ductility. ACI Structural Journal 1999;96(5). [11] Manfredi G, Fabbrocino G, Cosenza E. Modelling of steel–concrete composite beams under negative bending. ASCE Journal Of Engineering Mechanics 1999;125(6) [ISSN 0733-9399]. [12] Bonacci JF, Wight JK. Displacement-based assessment of reinforced concrete frames in earthquake—Mete A. Sozen Symposium. ACI Publication SP 162, 1996. p. 117–133.